The invention relates to the general field of telecommunications.
The invention relates more particularly to transmitting digital signals based on multicarrier modulation of the orthogonal frequency division multiplex-offset quadrature amplitude modulation (OFDM-OQAM) type in the context of systems having a number of transmit antennas N greater than or equal to 1 and a receive antenna. Such systems are also known as single-input single-output (SISO) systems in the presence of a single transmit antenna and a single receive antenna, or as multiple-input single-output (MISO) systems in the presence of a plurality of transmit antennas and a single receive antenna.
The invention can be applied to the field of wired communications (e.g. x digital subscriber line (xDSL), power line communication (PLC), optical fiber, etc.), or wireless communications (e.g. beyond third generation (B3G) systems, wireless local area network (WLAN) systems, etc.), for uplinks (terminal to an access point/base station) and/or for downlinks (access point/base station to terminal).
In known manner, the noise associated with the imperfections of communications systems and with the physical nature of the components used in such systems (such as the antennas, for example) affects the transmission of digital signals. Such signals are also subjected to deformation when they propagate between the transmit antenna (s) and the receive antenna (e.g. via an air channel). In the description below, the concept of a transmission or propagation channel between a transmit antenna and a receive antenna is used to cover not only the effects of the medium via which the digital signal propagates between the transmit antenna and the receive antenna (e.g. wireless channel or wired channel), but also the effects induced by the transmit and receive antennas on the digital signal.
The invention has a preferred but non-limiting application in the field of data transmission over so-called frequency selective transmission channels (multipath channels) with variations over time that are relatively slow.
In known manner, the frequency selectivity of a transmission channel is associated with the digital signal that is it desired to transmit over the channel: it is representative of the fact that the digital signal has frequency components that are attenuated differently by the transmission channel. In other words, this phenomenon appears when the bandwidth of the signal that is to be transmitted is much greater than the coherence bandwidth of the transmission channel, where the coherence bandwidth of a channel is defined as the minimum bandwidth at which two attenuations of the channels are independent. Compensating for the effects of the distortions introduced by multipath channels is then performed with the help of equalization techniques.
In this context, it is generally accepted that multicarrier transmission systems (or multicarrier modulation (MCM) systems), such as OFDM systems in particular, present numerous advantages. By transmitting data over a plurality of carrier frequencies in parallel (i.e. frequency multiplexing on a plurality of carrier frequencies also referred to as carriers or subcarriers), multicarrier transmission systems take the information that is for transmission at a high data rate and spread it over a large number of individual subbands that are modulated at low rates. This advantageously makes it possible to replace the step of equalizing a multipath channel, which may turn out to be complex in the time domain for single-carrier systems, with a step of performing equalization that is simple (having one coefficient per carrier) and that is performed in the frequency domain.
Orthogonal frequency division multiplexing (OFDM) is a multicarrier modulation technique that imposes a constraint of orthogonality between the subcarriers in order to limit interference between carriers (known as intercarrier interference (ICI)), while optimizing spectrum occupation. OFDM also benefits from implementation schemes that are simple and effective on the basis of inverse fast Fourier transforms (IFFTs) on transmission and of fast Fourier transforms (FFTs) on reception.
The constraint of orthogonality between the subcarriers is ensured by using a rectangular function (Π gate function) for shaping the multicarrier channel. Adding redundancy in the form of a cyclic prefix (CP) or of a guard interval (e.g. made of zeros) at the output from the inverse fast Fourier transform also makes it possible to limit the distortion due to the interference introduced by the channel between symbols (known as intersymbol interference) (ISI)), and been carriers.
An OFDM signal sCP-OFDM[k] with a cyclic prefix (a CP-OFDM signal) in baseband, with discrete time, and with M subcarriers at an instant kTe, where Te designates the sampling period, is expressed by the following equation:
            s              CP        ⁢                  -                ⁢        OFDM              ⁡          [      k      ]        =            ∑              m        =        0                    M        -        1              ⁢                  ⁢                  ∑                  n          =                      -            ∞                                    +          ∞                    ⁢                          ⁢                        c                      m            ,            n                          ⁢                  Π          ⁡                      [                          k              -                              n                ⁡                                  (                                      M                    +                                          L                      CP                                                        )                                                      ]                          ⁢                  ⅇ                      j            ⁢                                          2                ⁢                π                            M                        ⁢            mk                              where j2=−1, Π designates a gate function of duration M, cm,n is a complex symbol (e.g. a symbol obtained by quadrature amplitude modulation (QAM)) transmitted over the carrier m at instant n, and LCP is the length of the cyclic prefix in number of samples.
Nevertheless, although adding a cyclic prefix (or a guard interval) of length LCP longer than the greatest length of the channel makes channel equalization easier by avoiding problems of ISI, it gives rise to a loss of spectrum efficiency that increases with increasing length of the cyclic prefix (or guard interval). The cyclic prefix or guard interval that is added does not convey any useful information in order to guarantee that the information that is received and processed on reception comes from a single multicarrier symbol.
In order to mitigate that drawback, it is known to make use of modulation of the orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) type. On each subcarrier, this modulation makes use of a complex QAM symbol cm,n being resolved (decomposed) into a pair of real symbols constituted by the real part (cm,n) and the imaginary part ℑ(cm,n) of the complex symbol cm,n applied to two half-symbol times. The real and imaginary parts of the complex symbols that are to be transmitted are also offset by one half-symbol time between two successive subcarriers. This decomposition into real symbols advantageously makes it possible to relax the constraint of orthogonality between the subcarriers to the domain of reals, thereby facilitating the design of orthogonal functions for shaping the multicarrier signal (also known as prototype functions or filters) that are thoroughly localized in terms of frequency and time.
The OFDM/OQAM signal sOFDM-OQAM[k] in baseband and in discrete time for M subcarriers at the instant kTe, where Te designates the sampling period, can thus be expressed in the following form:
            s              OFDM        ⁢                  -                ⁢        OQAM              ⁡          [      k      ]        =            ∑              m        =        0                    M        -        1              ⁢                  ⁢                  ∑                  n          =                      -            ∞                                    +          ∞                    ⁢                          ⁢                        a                      m            ,            n                          ⁢                                            f              [                              k                -                                  n                  ⁢                                                                          ⁢                                      M                    2                                                              ]                        ⁢                          ⅇ                              j                ⁢                                                                  ⁢                                                      2                    ⁢                    π                                    M                                ⁢                                  m                  ⁡                                      (                                          k                      -                                                                        (                                                      LF                            -                            1                                                    )                                                ⁢                                                  /                                                ⁢                        2                                                              )                                                                        ⁢                          ⅇ                              j                ⁢                                                                  ⁢                                  ϕ                                      m                    ,                    n                                                                                            ︸                                          f                                  m                  ,                  n                                            ⁡                              [                k                ]                                                        where the coefficients am,n are real coefficients (e.g. pulse amplitude modulation (PAM) symbols), f[ ] designates a prototype filter of length LF, and φm,n designates a phase term, e.g. selected to be equal to
      π    2    ⁢            (              m        +        n            )        .  
Thus, the OFDM/OQAM modulation is freed from the presence of a guard interval or a cyclic prefix by a suitable selection of the prototype filter f modulating each subcarrier of the signal in such a manner as to ensure that each of these subcarriers is well localized in time and in frequency, and satisfying a real orthogonality constraint between the subcarriers that is expressed as follows:
      ℜ    ⁢          {              〈                              f                          m              ,              n                                ,                      f                                          m                ′                            ,                              n                ′                                                    〉            }        =            ℜ      ⁢              {                              ∑                          k              =                              -                ∞                                                    +              ∞                                ⁢                                          ⁢                                                    f                                  m                  ,                  n                                            ⁡                              [                k                ]                                      ⁢                                          f                                                      m                    ′                                    ,                                      n                    ′                                                  *                            ⁡                              [                k                ]                                                    }              =                  δ                  m          ,                      m            ′                              ⁢              δ                  n          ,                      n            ′                              where <g,h> designates the scalar product between g and h. The scalar product <fm,n, fm′,n′> is thus a pure imaginary number for (m,n)≠(m′,n′). For simplification purposes in the description below, the following notation is used:fm,np,q=−−jfm,n,fp,q
By way of example, a known prototype filter that satisfies this constraint is the prototype filter obtained from the IOTA function as described in patent application FR 2 733 869, or the TFL1 prototype filter used in the document by C. Lélé et al. entitled “Channel estimation methods for preamble-based OFDM/OQAM modulations”, European Wireless, April 2007 (given reference D1 in the description below).
Nevertheless, in spite of using a prototype filter that is well localized in time and in frequency, OFDM/OQAM modulation, by construction, produces an imaginary intrinsic interference term. Using conventional assumptions concerning the transmission model (channel invariant in a neighborhood ΩΔm,Δn departing by no more than ±Δm, ±Δn around each time-frequency point of coordinates (m,n), prototype filter f well localized in time and in frequency and shifted from the prototype filter that are invariant for a maximum delay of the channel equal to a determined number of samples), it is easy to show that for a SISO system, after transmission over a frequency selective channel with disturbance by additive noise written η, the demodulation signal can be written in the following form:ym,n=hm,n(am,n+jam,n(i))+Jm,n+ηm,n where:                hm,n designates the value of the complex channel on the subcarrier m at instant n;        ηm,n designates the noise component at instant n on the subcarrier m;        jam,n(i) designates a purely imaginary intrinsic interference term affecting the symbol am,n and depending on its neighboring symbols at the instant n as given by:        
      a          m      ,      n              (      i      )        =            ∑                                    (                          p              ,              q                        )                    ⁢                      εΩ                                          Δ                ⁢                                                                  ⁢                m                            ,                              Δ                ⁢                                                                  ⁢                n                                                    -                  (                      0            ,            0                    )                                          ⁢                  ⁢                  a                              m            +            p                    ,                      n            +            p                              ⁢                        〈          f          〉                          p          ,          q                          m          ,          n                    with fm,np,q=−jfm,n,fp,q; and                Jm,n designates an interference term created by symbols situated outside the neighborhood of the symbol am,n.        
Calculation of the interference terms is described in greater detail in document D1 and is not repeated herein.
If firstly the prototype filter f is well localized in frequency and in time, and if secondly the channel is not exclusively frequency selective and/or the signal-to-noise ratio is not too great, the term Jm,n can be ignored compared with the noise term ηm,n. It should be observed that this approximation is appropriate in a large number of scenarios that are to be encountered in practice. The demodulated signal can then be approximated as follows:ym,n≈hm,n(am,n+jam,n(i))+ηm,n 
Starting from this approximation, various techniques can then be envisaged on transmission and on reception for eliminating the intrinsic interference term am,n(i) for a SISO system. By way of example, one such technique, mentioned in document D1, consists in using a ZF equalizer on reception having one coefficient per carrier applied to the real part of the demodulated signal ym,n.
Nevertheless, although those techniques are effective for a SISO system (i.e. a system with a single transmit antenna and a single receive antenna), they are not easily transposable to a multiantenna system of the MISO type, and in particular to a system making use of space-time coding, such as for example the orthogonal coding scheme of coding rate 1 defined for two transmit antennas in the document by S. Alamouti entitled “A simple transmit diversity technique for wireless communications”, IEEE Journal of Selected Areas Communication, 1988, No. 16, pp. 1451-1458.
The space-time coding scheme produced by Alamouti corresponds to an open loop coding system in which two successive complex symbols s1 and s2 are transmitted over two transmit antennas in compliance with the following code matrix:
      G    ⁢                  ⁢    2    =            [                                                  s              ⁢                                                          ⁢              1                                                                          -                s                            ⁢                                                          ⁢                              2                *                                                                                        s              ⁢                                                          ⁢              2                                                          s              ⁢                                                          ⁢                              1                *                                                        ]              ︷                        antennas          ⁢                                          ↓                ,                  time          →                    where s* designates the complex conjugate of the symbol s. The rows of the matrix G2 give the symbols transmitted over the various transmit antennas: thus, the symbols s1 and then −s2* are transmitted over the first antenna, while the symbols s2 and s1* are transmitted over the second antenna.
The coding matrix G2 is a complex orthogonal matrix, i.e. G2G2H=I, where I designates the identity matrix of dimensions 2×2 and H designates the Hermetian operator. Thus, the coding scheme proposed by Alamouti advantageously offers a coding rate of 1 while ensuring on reception that the symbols transmitted over each antenna are decoupled, thus making it possible to use simple linear decoding with maximum likelihood.
Applying the Alamouti coding scheme to OFDM modulation leads to the coding matrix GC2 being rewritten, e.g. in the following form:
      GC    ⁢                  ⁢    2    =      [                                        c                          m              ,              n                                                            -                          c                              m                ,                                  n                  +                  1                                            *                                                                        c                          m              ,                              n                +                1                                                                          c                          m              ,              n                        *                                ]  where cm,n designates the complex symbol transmitted at an instant n on a subcarrier m.
A similar coding scheme can also be defined for modulation of OFDM-OQAM type, taking account of the fact that, as mentioned above, OFDM-OQAM modulation resolves each complex symbol cm,n into a pair of real symbols ((cm,n) and ℑ(cm,n)) that are spaced apart on the same subcarrier by a half symbol time T/2 (where T designates the duration of a complex symbol), and that are also offset by a half-symbol time between two consecutive subcarriers. Using the notation am,2n+k,i for the real symbols transmitted over the carrier m at four successive instants (2n+k)T/2, k=0, . . . , 3, over antenna i, i=0,1, it is possible to define the following orthogonal coding scheme:am,2n,0=(cm,2n)am,2n,1=(cm,2n+1)am,2n+1,0=ℑ(cm,2n)am,2n+1,1=ℑ(cm,2n+1)am,2n+2,0=−((cm,2n+1)*)=−(cm,2n+1)=am,2n,1 am,2n+2,1=((cm,2n)*)=(cm,2n)=am,2n,0 am,2n+3,0=ℑ((cm,2n+1)*)=ℑ(cm,2n+1)=am,2n+1,1 am,2n+3,1=ℑ(cm,2n))=−ℑ(cm,2n)=am,2n+1,0 
In similar manner, for SISO, if hm,n,i designates the gain of the complex channel between the transmit antenna i and the receive antenna for the subcarrier m at instant nT/2, and if it is assumed that this gain is constant between the instants 2nT/2 and (2n+3)T/2, then the signal received on the receive antenna for the subcarrier m is given by:ym,2n=hm,2n,0(am,2n,0+jam,2n,0(i))+hm,2n,1(am,2n,1+jam,2n,1(i))+nm,2n,0,ym,2n+1=hm,2n,0(am,2n+1,0+jam,2n+1,0(i))+hm,2n,1(am,2n+1,1+jam,2n+1,1(i))+nm,2n+1,1,ym,2n+2=hm,2n,0(am,2n+2,0+jam,2n+2,0(i))+hm,2n,1(am,2n+2,1+jam,2n+2,1(i))+nm,2n+2,0,ym,2n+3=hm,2n,0(am,2n+3,0+jam,2n+3,0(i))+hm,2n,1(am,2n+3,1+jam,2n+3,1(i))+nm,2n+3,1,where am,n,i(i) designates the intrinsic interference affecting the real symbol am,n,i depending on its neighboring symbols at instant n.
By writing:zm,2n=ym,2n+jym,2n+1 and zm,2n+1=ym,2n+2+jym,2n+3 the following expression can be obtained from the above equations after performing a few calculations that are described in greater detail in document D1:
            [                                                  z                              m                ,                                  2                  ⁢                  n                                                                                                                        (                                  z                                      m                    ,                                                                  2                        ⁢                        n                                            +                      1                                                                      )                            *                                          ]              ︸                        z                      2            ⁢            n                          _              =                              [                                                                      h                                      m                    ,                                          2                      ⁢                      n                                        ,                    0                                                                                                h                                      m                    ,                                          2                      ⁢                      n                                        ,                    1                                                                                                                        h                                      m                    ,                                          2                      ⁢                      n                                        ,                    1                                    *                                                                              -                                      h                                          m                      ,                                              2                        ⁢                        n                                            ,                      0                                        *                                                                                ]                          ︸                                    Q                              2                ⁢                n                                      _                              ⁢                        [                                          ⁢                                                                      c                                      m                    ,                                          2                      ⁢                      n                                                                                                                                            c                                      m                    ,                                                                  2                        ⁢                        n                                            +                      1                                                                                                    ]                          ︸                                    c                              2                ⁢                n                                      _                                +                            [                                                                      h                                      m                    ,                                          2                      ⁢                      n                                        ,                    0                                                                                                h                                      m                    ,                                          2                      ⁢                      n                                        ,                    1                                                                              0                                            0                                                                    0                                            0                                                              h                                      m                    ,                                          2                      ⁢                      n                                        ,                    1                                    *                                                                              -                                      h                                          m                      ,                                              2                        ⁢                        n                                            ,                      0                                        *                                                                                ]                          ︸                                    K                              2                ⁢                n                                      _                              ⁢                        [                                                                      x                                      m                    ,                                          2                      ⁢                      n                                        ,                    0                                                                                                                        x                                      m                    ,                                          2                      ⁢                      n                                        ,                    1                                                                                                                        x                                      m                    ,                                                                  2                        ⁢                        n                                            +                      2                                        ,                    0                                                                                                                        x                                      m                    ,                                                                  2                        ⁢                        n                                            +                      2                                        ,                    0                                                                                ]                          ︸                                    x                              2                ⁢                n                                      _                                +                  [                                                            μ                                  m                  ,                                      2                    ⁢                    n                                                                                                                          μ                                  m                  ,                                                            2                      ⁢                      n                                        +                    1                                                  *                                                    ]                    ︸                              μ                          2              ⁢              n                                _                    where:                the matrix Q2n is an orthogonal matrix;        μ2n is a noise component; and        x2n is a vector with components that are linear combinations of intrinsic interference terms.        
This expression shows that unlike the SISO situation, in a MISO system using Alamouti type coding, the signal received on the receive antenna presents an intrinsic interference term K2nx2n that, even in the absence of noise, is difficult to eliminate.
Solutions exist in the represent state of the art for remedying this drawback. Nevertheless, most of them require either complex reception schemes to be implemented, or else the addition of a cyclic prefix, thereby giving rise to a loss of spectrum efficiency.
There therefore exists a need for an OFDM-OQAM type transmission scheme that does not lead to a loss of spectrum efficiency and that can be used in the context of a SISO system or a MISO system without requiring complex reception algorithms to be performed.